Polynomial representation growth and the congruence subgroup problem

By Alexander Lubotzky, B. Martin. 2004

57 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a752981d8a1933d524fecf2ddb0c714d253c3a56

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Representation growth and rational singularities of the moduli space of local systems (2013, background): “In [40], the authors prove thatα( ) ≤ 3dimG.”
Zeta functions of groups and rings (2007, methodology): “(7) The formalism of zeta functions has been used to count representations of arithmetic and p-adic analytic groups in the papers [37] of B.”
Representation Growth of Linear Groups (2006, methodology): “ ﬁnite index subgroup Γ0 of Γ (with Γ0 = Γ if ker(G\(OS) →G(OˆS)) = {e}) A(Γ0) = G(C)#S∞ × Y v/∈S Lv where Lv is open in G(Ov) and equal to it for almost all v. Finally, we mention the main result of [LuMr]: Theorem 3.4 (Lubotzky-Martin [LuMr]). If Γ = G(OS) has the CSP then rn(Γ) is polynomially bo”
Commutator maps, measure preservation, and T-systems (2007, background): “Recall that the representation growth of G is the series {rn(G)}, where rn(G) is the number of irreducible representations of G of degree n. See [ LM , Ja] for background.”
Zeta function of representations of compact p-adic analytic groups (2005, methodology): “Following [20], we call rn(G) the representation growth function of G.”
Character Degrees and Random Walks in Finite Groups of Lie Type (2005, result): “See [1, 32, 23] for some recent results on rnðKÞ and K .”
Representation zeta functions of compact p-adic analytic groups and arithmetic groups (2010, background): “k, for a ﬁnite set Sof places of kincluding all the archimedean ones. Let Γ be of this form. Lubotzky and Martin showed that Γ has PRG if and only if Γ has the Congruence Subgroup Property (CSP); cf. [38]. Suppose that Γ possesses these properties. Then according to a result of Larsen and Lubotzky (”